When it comes to CC Sabathia, the Yankees are running out of answers. Out of theories. Out of positive spin.

Worst of all, however, may be the one element of which they are not even remotely running out: Time.

The big lefty registered arguably his worst start as a Yankee on Sunday, getting clobbered and booed in a 5-1 loss to the Rays at Yankee Stadium. Sabathia lasted just 3 ²/₃ innings, allowing five runs and 10 hits, and afterward, Yankees pitching coach Larry Rothschild revealed he knew something was amiss when Sabathia threw poorly in his pregame warmup.

These 2014 Yankees, their current perch atop the American League East notwithstanding, look imperiled as long as their highly paid veterans Sabathia and Hiroki Kuroda pitch as poorly as they have recently. Yet the Sabathia dilemma stretches well beyond 2014. It goes back to last year and stretches at least through 2016, if not 2017.

“Going through this adversity has been the toughest part of my baseball career by far,” the always accountable Sabathia said. “But I know I’ll come out of this a better pitcher for it.”

“This adversity” has lasted longer than many celebrity marriages. Since the start of the 2013 season, Sabathia holds a 4.94 ERA in 251 ²/₃ innings pitched. Of all major-league pitchers who have thrown 200-plus innings in the past season-plus, only two pitchers — Edinson Volquez (5.43) and Edwin Jackson (5.02) have tallied worse ERAs than the Yankees’ titular ace.

We’ve heard just about everything in this time span: Sabathia, whose velocity dropped precipitously, was recovering from his October 2012 surgery to remove a small bone spur from his left elbow. He was trying to pitch with his new weight loss. Sabathia himself admitted at the end of last season that, since he couldn’t overpower hitters like he once could, he needed to prepare more.

On Sunday, manager Joe Girardi said: “I still think he’s evolving into a different type of pitcher.”

Alas, evolution isn’t part of the Yankees’ business model, especially for a guy whom they’re paying $23 million this year and next year, followed by $25 million in 2016 and an easily attainable $25 million vesting option — essentially, he just has to stay healthy, and both he and the Yankees insist health is not an issue now — for 2017.

If this is really it for the 39-year-old Kuroda, then the Yankees can just kick him curbside this fall. If Sabathia, turning 34 in July, can’t find his desired consistency, though? It’s going to be a long, ugly path.

Sunday went down as especially ugly, with neither Sabathia’s sinker nor his changeup behaving themselves. As Sabathia noted, this one would be easier to write off if so many other starts hadn’t been subpar. And a high percentage of those starts fell into the “one bad inning” category, when Sabathia missed plenty of bats but couldn’t minimize damage when things went awry.

Shoot, Sabathia has 44 strikeouts against nine walks in 40 ²/₃ innings this season, so stat-geek common sense tells you he should level out eventually. Common sense plus knowledge of the man himself.

“It can turn at any time,” Rothschild said, even as he acknowledged Sabathia’s consistency has been absent for more than a year. “We’re all thinking that it will. I think he feels that it will. When you have someone as competitive as he is, there’s a good chance that we’ll get this straightened out.”

Nevertheless, the results and the overall numbers speak for themselves. Even going by the low standard of a quality start — at least six innings pitched and no more than three runs allowed — Sabathia hasn’t put together three consecutive such performances since last April, a span of 35 starts without a basic level of consistency.

You don’t bet heavily against Sabathia, and you appreciate him saying, of the booing that accompanied his fourth-inning departure, “I would’ve booed myself today, too.

“I know that what I’m doing is working,” he added. “I just need to get a little better at it.”

More than “a little” better, actually. Unless you think the Yankees have only “a little” riding on Sabathia rediscovering his old self — or even something just closer to that — sooner than later.